Geometry & Topology

The Gromov width of $4$–dimensional tori

Janko Latschev, Dusa McDuff, and Felix Schlenk

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Let ω be any linear symplectic form on the 4–torus T4. We show that in all cases (T4,ω) can be fully filled by one symplectic ball. If (T4,ω) is not symplectomorphic to a product T2(μ)×T2(μ) of equal sized factors, then it can also be fully filled by any finite collection of balls provided only that their total volume is less than that of (T4,ω).

Article information

Geom. Topol., Volume 17, Number 5 (2013), 2813-2853.

Received: 27 September 2012
Accepted: 13 June 2013
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57R17: Symplectic and contact topology 57R40: Embeddings
Secondary: 32J27: Compact Kähler manifolds: generalizations, classification

Gromov width symplectic embeddings symplectic packing symplectic filling tori


Latschev, Janko; McDuff, Dusa; Schlenk, Felix. The Gromov width of $4$–dimensional tori. Geom. Topol. 17 (2013), no. 5, 2813--2853. doi:10.2140/gt.2013.17.2813.

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